Texture mapping and rendering

CS 248 - Introduction to Computer Graphics
Autumn Quarter, 2008
Marc Levoy
Lecture notes for Thursday, October 23 (finished Tuesday, Oct. 28)

Table of contents:

• Texture mapping
  • Coordinate systems
  • Common mapping pipelines
  • A practical backward mapping algorithm if f is linear
• Texture rendering
  • Texture rendering is image resampling
  • Review of resampling pipeline
  • Some common warps
  • Typical approximations
• Precomputed filtering
  • The costs of texture resampling
  • Mipmapping
  • Summed area tables

As mentioned in class, the "gather" operation, i.e. gathering values from nearby texels (texture pixels), is only required if the texture is discrete. For procedural textures, one can typically request a value at any desired floating point (u,v) position. On the other hand, if we are minifying the texture, as described later in these notes, then one might still need to gather many samples in order to avoid aliasing, unless of course the texture generation procedure prefilters the texture internally.

I didn't cover these other filters in class, and I won't hold you responsible for them. There is some discussion of them in Paul Heckbert's article, which I handed out. If you're interested in reading more about texture mapping and filters, Heckbert's Master's thesis (available from his home page) makes excellent reading.